Recent research in provably secure neural linguistic steganography has overlooked a crucial aspect: the sender must detokenize stegotexts to avoid raising suspicion from the eavesdropper. The segmentation ambiguity problem, which arises when using language models based on subwords, leads to occasional decoding failures in all neural language steganography implementations based on these models. Current solutions to this issue involve altering the probability distribution of candidate words, rendering them incompatible with provably secure steganography. We propose a novel secure disambiguation method named SyncPool, which effectively addresses the segmentation ambiguity problem. We group all tokens with prefix relationships in the candidate pool before the steganographic embedding algorithm runs to eliminate uncertainty among ambiguous tokens. To enable the receiver to synchronize the sampling process of the sender, a shared cryptographically-secure pseudorandom number generator (CSPRNG) is deployed to select a token from the ambiguity pool. SyncPool does not change the size of the candidate pool or the distribution of tokens and thus is applicable to provably secure language steganography methods. We provide theoretical proofs and experimentally demonstrate the applicability of our solution to various languages and models, showing its potential to significantly improve the reliability and security of neural linguistic steganography systems.